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Up to 35,000 people, mostly Turks, rallied in German city of Cologne on Saturday to demonstrate their support of Erdogan. (Photo: orangejack)

"If visa liberalisation does not follow, we will be forced to back away from the deal on taking back [refugees] and the agreement of 18 March," he told Germany's daily Frankfurter Allgemeine Zeitung over the weekend.

Cavusoglu said the waivers should ideally be introduced in October.

Once granted, it would allow Turkish nationals to visit any of the passport-free Schengen states without a visa.

The March agreement was designed to stop migrants, mostly from Syria, from crossing from Turkey into Greece.

In exchange, Syrian refugees in Turkey are set to receive €3 billion in EU humanitarian aid. Both sides also agreed to speed up EU membership talks and allow Turks visa-free travel in Schengen countries.

Thousands were arriving on the Greek islands on a daily basis at the height of the crisis last year. Those numbers dropped to double figures following the March deal.

'Constant and apparently increasing flow'

But reports are emerging of an increase in crossings since last month's failed attempt to overthrow Turkey's autocratic president Recep Tayyip Erdogan.

Greek authorities are raising the alarm over a “constant and apparently increasing flow” of people making the crossings.

Over 1,000 have crossed from Turkey to the Greek islands since the military coup attempt on 15 July.

The islands are now hosting some 9,400 men, women, and children who are seeking asylum - including eight Turkish soldiers.

European Commission president Jean-Claude Juncker is also worried.

He told an Austrian daily Kurier on Friday that the "risk is great" the agreement with Turkey would fail.

"The success of the pact so far is fragile. President Erdogan has several times hinted he wants to terminate the agreement,” he said.

The EU commission had in the wake of the coup said it would abide by the visa waiver plan.

Lifting the restriction would first require lawmakers in Ankara to rewrite an anti-terrorism law. The EU says the law's definition of terrorism is too broad and allows authorities to target journalists and opposition MPs.

Turkey's prime minister Binali Yıldırım in June said Ankara would not budge on the legislation.

"Amendments to the anti-terror law under these conditions are out of question for us, even if changes would lead to visa exemptions being granted,” he had said at the time.

Ankara continues purge

But the failed coup on 15 July has since seen tens of thousands people swept up in a government-led purge.

Charities, teachers, university deans, and top military brass among others have been forced to resign or detained.

Last week, Ankara announced it would shut down three news agencies, 16 TV channels, 23 radio stations, 45 newspapers and 15 magazines.

It also issued arrest warrants for 47 journalists and media executives.

Up to 35,000 people, mostly Turks, rallied in German city of Cologne on Saturday to demonstrate their support of Erdogan.

Children out of school and vulnerable to radicalisation, asylum claimants pushed back from Greece, and refugees forbidden from entering from Syria - a new report paints a bleak picture of the situation in Turkey.

The EU border and coast guard agency, or Frontex, has launched a new naval operation called Themis. The operation replaces its surveillance Triton mission but with a bigger emphasis on security and intelligence gathering.